Here, we are not interested in the stability of dynamical systems but
the resilience of networks. In [1]} the resilience of
a very basic model for transportation networks was investigated
via introducing a “backup capacity” (see below) and using
large-deviation techniques. The model in [1]} assumes
that one unit of some “quantity” is transported between all
pairs of nodes along shortest paths. In the present work, we study
a very different model, still quite simple but designed for modelling
power grids, based on the laws of electricity. Specifically, we
introduce a power flow model on networks based on the
fixed points of a Kuramoto-like model [3]}, [4]} and a
linearized DC power flow model (see e.g., [5]}) as used in
electrical engineering, respectively.
